Three people have died and thousands evacuated from their homes as flooding caused by the remains of tropical cyclone Oswald battered the east coast of Australia.

High winds, including mini-tornadoes, and torrential rain have lashed large parts of southern Queensland and are moving south to the country’s most populous state, New South Wales, with Sydney expected to be hit on Monday night.

In Queensland, all eyes were on the city of Bundaberg, 300km (190 miles) north of Brisbane, as it prepared for unprecedented flooding after the Burnett river burst its banks. Mandatory evacuation orders were issued in parts of the city, which has a population of 100,000. Helicopters worked throughout Monday to rescue people cut off by rising waters which were flowing at more than 70km/h, making rescue by boat virtually impossible.

“We believe there is an imminent danger of people being killed and drowned, so that’s why we’re making the mandatory evacuations,” Bundaberg’s police superintendent, Rowan Bond, told the Australian newspaper.

The Burnett river is projected to reach a peak of 10 metres, more than 2 metres above the peak of flooding two years ago when more than 30 people died across Queensland in floods that covered an area the size of France and Germany combined.

The Queensland state premier, Campbell Newman, who was the lord mayor of Brisbane during the 2011 floods, said his state was facing a major disaster crisis.

He said “To those in the grip of the disaster, I say to you, you are not alone. We are going to do everything we can to protect you, to rescue you and to stand with you in the days, weeks and months ahead. Together we will get through this,” he said.

Newman warned that the speed of the floodwaters in Bundaberg was so great, there was a risk that some houses may be swept away.

“This is a very real prospect. In the 1893 floods in Brisbane, houses were literally lifted off their stumps and then swept down the Brisbane river and that is a real prospect this afternoon or tonight in north Bundaberg,” he said.

In the state’s capital, Brisbane, hundreds of roads were closed and 220,000 homes were without power. The Brisbane river, which deluged thousands of homes two years ago, broke its banks in several areas and water entered some low-lying areas, which were badly flooded in 2011. The river is expected to peak on Tuesday but nearly 7 metres lower than it did two years ago.

Evacuations were taking place in other parts of southern Queensland, including in the Lockyer valley west of Brisbane, where small communities were devastated when an inland tsunami up to 7-8 metres high tore through small rural communities in January 2011.

The prime minister, Julia Gillard, said the floods had “broken a lot of hearts” in Queensland, and were particularly difficult for Lockyer valley communities, with many facing a second flood in two years.

“Psychologically, for people who went through the devastating events in the … Lockyer valley, I think this is a particularly difficult time,” she said.

Further south on Queensland’s Gold Coast, 70km south of Brisbane, more than a metre of rain fell in the 24 hours to 9am on Monday. Out to sea waves of 10 metres in height were recorded.

The weather system is what remains of tropical cyclone Oswald, which started last week in the Gulf of Carpentaria, at the very top of Australia. As the system moved south across the New South Wales border, rainfall of up to 300mm was expected in the north of the state. Winds of over 100km/h have been recorded in holiday towns including Byron Bay, close to the Queensland border.

The wet weather follows a summer of unprecedented heat across large parts of Australia. Just over a week ago, emergency services were issuing fire warnings. Sydney experienced its hottest day on record in January, with the mercury peaking at 46.5C (115.7F). Parts of the southern state of Victoria are still on bushfire alert.